Abstract We present a number of exact cosmological solutions in the SU(1, 1)/U(1) “no-scale” theory of supergravity. We show that the auxiliary superfield acts as a negative stress and this permits the existence of a wide class of solutions which avoid the singularities that appear in the cosmological models of general relativity. However, by way of compensation, the dilation field always evolves so as to alter the sign of the coupling of matter to gravity in the vicinity of any expansion minimum or singularity. Moreover, the coupling of the dilation to any conventional matter sources present in the universe which is imposed by the theory does not appear to permit either power-law or exponential inflation to take place. The evolution of the mean expansion scale-factor is controlled by the auxiliary field density rather than by any conventional matter or inflaton fields present in the universe. These results indicate that classical “no-scale” supergravity theory (or at least its SU(1,1)/U(1) bosonic incarnation) may not provide acceptable models of the early universe.